Fish farming is growing but is also facing challenges regarding economic viability and environmental sustainability. Selective breeding could enhance the sustainability of fish farming by changing animal performances. Thus, our aim was to develop sustainable breeding goals by using economic (EV) or environmental values (ENV) to weigh the traits to improve. EV and ENV represent the economic and environmental impacts of improving a trait. They were calculated using a bioeconomic model combined with a life cycle assessment. We showed that the EV and ENV of traits change with the factor constraining the production of the farm. It suggests that breeding goals should be finely tuned according to the limiting factor to maximize economic or environmental responses. In addition, we showed that improving feed conversion ratio is a major trait to improve because it always increases profit and decreases environmental impacts. We conclude that it is possible to develop breeding programs enhancing the sustainability of fish farming by improving the right trait in the right production system.